Rare Metals

, Volume 37, Issue 4, pp 290–299 | Cite as

Enhancing point defect scattering in copper antimony selenides via Sm and S Co-doping

  • Tian-Hua Zou
  • Wen-Jie Xie
  • Marc Widenmeyer
  • Xing-Xing Xiao
  • Xiao-Yin Qin
  • Anke Weidenkaff


Doping- and alloying-induced point defects lead to mass and strain field fluctuations which can be used as effective strategies to decrease the lattice thermal conductivity and consequently boost the performance of thermoelectric materials. Herein, we report the effects of Sm and S co-doping on thermoelectric transport properties of copper antimony selenides in the temperature range of 300 K < T < 650 K. Through the Callaway model, it demonstrates that Sm and S co-doping induces strong mass differences and strain field fluctuations in Cu3SbSe4. The results prove that doping with suitable elements can increase point defect scattering of heat-carrying phonons, leading to a lower thermal conductivity and a better thermoelectric performance. The highest figure of merit (ZT) of ~ 0.55 at 648 K is obtained for the Sm and S co-doped sample with nominal composition of Cu2.995Sm0.005SbSe3.95S0.05, which is about 55% increase compared to the ZT of pristine Cu3SbSe4.

Graphical Abstract


Thermoelectric Point defect scattering Cu3SbSe4 Lattice thermal conductivity 

1 Introduction

Thermoelectricity, a technology to convert heat into electricity directly, is a potential alternative to recover waste heat and partially solve the energy harvesting issue [1, 2, 3]. The conversion efficiency of a thermoelectric material is characterized by the figure of merit (ZT) defined as: \({\text{ZT}} = \frac{{S^{2} }}{\rho \kappa }T = \frac{{S^{2} }}{{\rho (\kappa_{\text{e}} + \kappa_{\text{L}} )}}T\), where S is the Seebeck coefficient, ρ the electrical resistivity, κ the total thermal conductivity, T the absolute temperature, κe the electronic thermal conductivity and κL the lattice thermal conductivity. According to the definition of ZT, a high-performance thermoelectric material should possess a low lattice thermal conductivity [4, 5]. For decades, the main strategy for designing high-performance thermoelectrics with low lattice thermal conductivity has been the introduction of nanostructures or point defects for scattering the heat-carrying phonons [6, 7, 8]. Nanostructures introduce large numbers of grain boundaries and can effectively scatter mid/long wavelength phonons and eventually significantly reduce κL [9, 10, 11, 12, 13, 14, 15]. Besides nanostructures, point defects also play a crucial role in diminishing κL. This is mainly attributable to mass fluctuations related to mass differences and strain field fluctuations related to interatomic coupling force differences between the introduced atom and the host lattice [16, 17].

Recently, Cu-based materials have attracted great attention due to their interesting electronic and thermal transport properties [18, 19]. Among them, Cu3SbSe4 (CSS), possessing a narrow band gap and a large Seebeck coefficient, has great potential for high-performance thermoelectric applications. While much effort has been devoted to tuning the charge carrier concentration (as to enhance the power factor) via doping on the Sb and Se sites [20, 21, 22, 23], less attention has been paid to decreasing κL of Cu3SbSe4. Skoug et al. [24, 25] report that the κL values of Cu3SbSe4 can be remarkably reduced via forming a Cu3SbSe4–Cu3SbS4 solid solution. Se and S both belong to the Group 16 elements but differ significantly in mass and electronegativity. S doping on the Se site can introduce strong mass and strain field fluctuations, resulting in a reduction of κL up to 76% at 80 K [25]. However, the κL values of Cu3SbSe4−yS y are still much higher than its estimated minimum thermal conductivity [25], indicating that there is still room for improvement. On the downside, the introduction of S is associated with a drastic reduction in the carrier concentration, resulting in a notably lower power factor. Thus, in order to take advantage of S doping-induced point defect phonon scattering, an extra hole donor should be introduced simultaneously to compensate the decrease in the carrier concentration.

In this work, Sm was introduced into the copper selenide matrix material, leading to extra hole donors in addition to S co-doping. Increasing Sm content leads to an enhancement of the hole concentration, which can be related to a complex defect chemistry and the introduction of additional point defects due to the large mass difference between Sm (150.36 g·mol−1) and Cu (63.546 g·mol−1). Here, we report the electrical and thermal transport properties of Sm/S co-doped Cu3SbSe4 and utilize the Callaway model to analyze the role that the co-doping plays in the reduction in the lattice thermal conductivity.

2 Experimental

Polycrystalline copper antimony selenides with nominal samarium and sulfur contents “Cu3−xSm x SbSe4−yS y (x = 0, 0.0050, 0.0075 and y = 0, 0.05, 0.10, 0.15)” were synthesized by melting high-purity elemental Cu (99.9%, powder), Sb (99.999%, shot), Se (99.999%, shot), Sm (99.999%, powder) and S (99.9%, powder) in respective stoichiometric proportions. The samples will be abbreviated in the following as CSS:(Sm-x,S-y) for co-doped CSS. The compositions described below are nominal composition, unless stated otherwise. All raw materials were sealed in quartz glass tubes under high vacuum. The tubes were heated to 1173 K for 12 h, cooled to 823 K and finally quenched in ice water. After quenching, samples were annealed at 623 K for 48 h to promote homogeneity. The ingots were pulverized into fine powders. Bulk samples were obtained by spark plasma sintering (SPS) for 5 min at 653 K under a pressure of 50 MPa. The relative densities of the bulk samples after SPS exceeded 94%.

X-ray diffraction (XRD) with Cu Kα radiation (Rigaku Smartlab, Cu Kβ filter) was used to ensure the phase purity of the CSS:(Sm-x,S-y) samples. Sample compositions were determined by inductively coupled plasma atomic emission spectroscopy (ICP-AES, Spectro Ciros CCD ICP-OES instrument). Scanning electron microscope (SEM, Hitachi S4800) was used to analyze the microstructures of the bulk samples after SPS. Electrical resistivity and thermopower were measured by a ZEM-3 (ULVAC-RIKO®) in helium atmosphere from 300 to 650 K. The uncertainty in the measurement of both the electrical conductivity and the thermopower is ± 7%. Hall coefficients were measured on a physical property measurement system (PPMS, Quantum Design®) in a magnetic field up to ± 0.5 T at room temperature. The estimated error of the Hall coefficient is within ± 10%. The thermal diffusivities (α) were measured on disk samples (2–3 mm in thickness) with a NETZSCH LFA-457 apparatus in the temperature range of 300–650 K in argon atmosphere. The thermal conductivities (κ) were calculated according to κ = DCpα, where Cp is the heat capacity obtained by the Dulong–Petit law, and D is the density measured using the Archimedes method. The uncertainty of the thermal conductivity is ± 10%.

3 Results and discussion

3.1 Crystal structure and microstructure

XRD patterns of the CSS:(Sm-x,S-y) samples are shown in Fig. 1a. All diffraction reflections can be well indexed to the tetragonal Cu3SbSe4 structure (standard JCPDS No. 85-0003; space group \(I\bar{4}2m\)), revealing no obvious impurity phases in the produced specimens. The microstructure of SPSed bulk samples was observed by SEM, and the typical microstructure of fresh fracture surface is presented in Fig. 1b. The grain size of SPSed bulk sample is around 10–30 µm, and the sample looks very dense. Secondary and backscattered electron (BSE) images of polished surface are shown in Fig. 1c, d, respectively. No obvious second phase can be detected, and the composition is homogenous in microscale.
Fig. 1

a XRD patterns of CSS:(Sm-x,S-y) samples: (1) PDF No. 85-0003, (2) Cu3SbSe4, (3) Cu2.9925Sm0.0075SbSe4, (4) Cu2.975Sm0.025SbSe4, (5) Cu3SbSe3.95S0.05, (6) Cu2.995Sm0.005SbSe3.95S0.05, (7) Cu2.9925Sm0.0075SbSe3.95S0.05, (8) Cu3SbSe3.9S0.1, (9) Cu2.995Sm0.005SbSe3.9S0.1, (10) Cu2.9925Sm0.0075SbSe3.9S0.1, (11) Cu3SbSe3.85S0.15, (12) Cu2.995Sm0.005SbSe3.85S0.15 and (13) Cu2.9925Sm0.0075SbSe3.85S0.15; b SEM image of typical microstructure of fresh fracture surface of SPSed Cu2.975Sm0.025SbSe4; c secondary electron images of polished surface of SPSed Cu2.975Sm0.025SbSe4; d BSE image of polished surface of SPSed Cu2.975Sm0.025SbSe4 (black particles on surface being polishing agent Al2O3)

3.2 Electrical transport properties

The temperature dependence of the electrical resistivity of the Sm and S co-doped samples is presented in Fig. 2. For instance, because S doping reduces the carrier concentration and also enhances impurity scattering, the electrical resistivity of the only S-doped samples is larger than that of the pristine sample at room temperature, as shown in Fig. 2a. When both S and Sm are doped in Cu3SbSe4, the observed electrical resistivity highly depends on the relative contents of S and Sm. As shown in Fig. 2c and d, at fixed S doping contents of y = 0.10 and 0.15, the electrical resistivity cannot be reduced with Sm contents (x) increasing. In contrast, when S doping content (y) is 0.05, enhanced Sm contents lead to a significant decrease in the resistivity, as shown in Fig. 2b. Room temperature physical properties of CSS:(Sm-x,S-y) samples are listed in Table 1. The results reveal that S doping reduces the hole concentration, which is consistent with the results in Refs. [24, 25]. Sm-doped samples reveal hole doping which might be a result of the Cu deficiency and/or Sm introduction into the matrix material. The increase in Sm content leads to a decrease in Cu content, as shown in Table 1. According to the results reported by Wei et al. [26], the Cu deficiencies can increase the carrier concentration of Cu3SbSe4 compound. Besides, Sm-doped samples possess high hole mobility. It is suspected that Sm doping might change the band structure of Cu3SbSe4 or/and the carrier scattering mechanisms. Such anomalous behavior is still under investigation. In the CSS:(Sm-x,S-y) system, the electrical resistivity is a tradeoff between increased charge carrier concentration and enhanced impurity scattering of charge carriers caused by the S/Sm doping.
Fig. 2

Temperature dependence of electrical resistivity of a CSS:(Sm-x,S-y) (x = 0 and y = 0, 0.05, 0.10, 0.15), b CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.05), c CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.10) and d CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.15)

Table 1

Nominal composition, ICP composition, carrier concentration (n) and carrier mobility (μ) of samples at room temperature

Nominal composition

ICP compositiona

n/1018 cm−3


















































aContents of Cu, Sm, Se and S being normalized to content of Sb

The temperature dependence of the thermopower of CSS:(Sm-x,S-y) is displayed in Fig. 3. Figure 3a shows the thermopower of Cu3SbSe4−yS y (y = 0, 0.05, 0.1, 0.15) specimens. Although S doping reduces the carrier concentration, the thermopower of only S-doped Cu3SbSe4 is quite close to that of the pristine sample. This tendency is quite similar to the results reported by Skoug et al. [24]. Figure 3b–d illustrates the temperature dependence of the thermopower of co-doped CSS:(Sm-x,S-y) samples, which significantly differs from that of the pristine sample. The thermopower of the co-doped samples decreases from room temperature to ~ 450 K and then increases slowly with the temperature increasing. It is suspected that Sm/S double doping may change the band structure of the host Cu3SbSe4.
Fig. 3

Temperature dependence of thermopower of a CSS:(Sm-x,S-y) (x = 0 and y = 0, 0.05, 0.10, 0.15), b CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.05), c CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.10) and d CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.15)

The power factor (PF = S 2 /ρ) is an indicator for the electrical transport properties of thermoelectric materials. The calculated PF of CSS:(Sm-x,S-y) is presented in Fig. 4. The highest PF is observed for Cu3SbSe3.9S0.1 (7.73 × 10−4 W·m−1·K−2) among the doped samples. However, because of the higher electrical resistivity and the lower thermopower values, no increase in PF of the doped samples compared with that of pristine Cu3SbSe4 can be observed in the entire temperature range studied.
Fig. 4

Power factor as a function of temperature of a CSS:(Sm-x,S-y) (x = 0 and y = 0, 0.05, 0.10, 0.15), b CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.05), c CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.10) and d CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.15)

3.3 Thermal transport properties and phonon scattering mechanisms

The temperature dependence of the thermal conductivity (κ) is shown in Fig. 5a. It can be seen that κ value of all specimens drops with temperature increasing and κ value of the doped samples is lower than that of the pristine sample. In order to clarify the effect of S and Sm doping on κ, Fig. 5c, d shows κ values of Cu3SbSe4−yS y (y = 0, 0.05, 0.10, 0.15), Cu3−xSm x SbSe3.95S0.05 (x = 0, 0.0050, 0.0075), Cu3−xSm x SbSe3.9S0.1 (x = 0, 0.0050, 0.0075) and Cu3−xSm x SbSe3.85S0.15 (x = 0, 0.005, 0.0075), respectively. As can be seen from Fig. 5c, κ value of all S-doped samples is lower than that of the pristine sample and decreases with S content increasing, which is consistent with the data in Refs. [24, 25]. Similarly, κ value of S/Sm double-doped samples CSS:(Sm-x,S-y), as shown in Fig. 5d, decreases with S and Sm content increasing.
Fig. 5

Temperature dependence of a total thermal conductivity and b lattice thermal conductivity of pristine and doped Cu3SbSe4 specimens; c temperature dependence of thermal conductivity for c CuSbSe4−yS y (x = 0 and y = 0, 0.05, 0.10, 0.15) and d CSS:(Sm-x,S-y) (x = 0, 0.005, 0.0075 and y = 0, 0.05)

The lattice contribution of the thermal conductivity, κL, that can be obtained from κL = κ − κe. κe is evaluated by the Wiedemann–Franz relation: κe = LσT, where σ is the measured electrical conductivity and L is the Lorenz number. The Lorenz number used here is obtained by fitting the measured thermopower (S) data via L = 1.5 + exp[− |S|/116] [27]. The κL of the doped samples is lower than that of the pristine sample, mainly resulting from the enhancement of phonon scattering, as revealed in Fig. 5b. Above room temperature, κL, is usually limited by a combination of Umklapp phonon–phonon (U), point defect (PD) and boundary (B) scattering. As shown in Fig. 5b, κL values of all samples follow a T−1 behavior in the whole measured temperature range, indicating that Umklapp phonon–phonon scattering is the dominating scattering mechanism. However, S/Sm co-doping-induced point defect scattering also plays an important role in depressing κL. For instance, κL of the S/Sm co-doped sample Cu2.9925Sm0.075SbSe3.85S0.15 is only 0.61 W·m−1·K−1 at 648 K, which is about 50% smaller than that of the pristine sample and very close to the theoretical minimum lattice thermal conductivity (κLmin), estimated by the Cahill’s formula and plotted in Fig. 5b [28].

In order to understand the phonon scattering mechanism of S/Sm co-doped Cu3−xSm x SbSe4−yS y , κL is estimated using the Callaway model [28, 29]:
$$\kappa_{\text{L}} = \frac{{k_{\text{B}} }}{{2\uppi^{2} v}}\left( {\frac{{k_{\text{B}} }}{\hbar }} \right)^{3} T^{3} \int_{0}^{{\theta_{\text{D}} /T}} {\tau (x)\frac{{x^{4} {\text{e}}^{x} }}{{({\text{e}}^{x} - 1)^{2} }}{\text{d}}x}$$
where x equals to ħω/kBT (ω is the phonon frequency), kB is the Boltzmann constant, v is the phonon velocity, θD is the Debye temperature and ħ is the reduced Planck constant. The Debye temperature and the phonon velocity used in our calculation are adopted from Ref. [30] and listed in Table 2.
Table 2

Average longitudinal acoustic velocity (vLA), transverse acoustic velocity (vTA/TA′), Grüneisen parameters (γTA/TA′/LA) and Debye temperatures (θDTA/TA′/LA) used in calculations from Ref. [30]




γ TA

γ TA′

γ LA













According to Matthiessen’s rule [28], the total combined relaxation time (τC) is estimated by the addition of the inverse relaxation times of the scattering processes, τ C −1  = Σ τ i −1 , where τ i is the phonon relaxation time of the ith scattering process. For the Umklapp phonon–phonon scattering mechanism, the inverse relaxation time (τU) can be described as [31]:
$$\tau_{\text{U}}^{ - 1} = \frac{{\hbar \gamma^{2} \varpi^{2} T}}{{Mv^{2} \theta_{\text{D}} }}\exp \left( { - \frac{{\theta_{\text{D}} }}{3T}} \right)$$
where \(\varpi\) is phonon frequency in radians per second, γ is the Grüneisen parameter and M the average molar mass. For the calculation, the reported values γ = 1.22 were chosen [30] (Table 2).
In a crystal lattice, point defect scattering originates from mass difference and strain fluctuations. The point defect scattering relaxation time (τPD) can be obtained through:
$$\tau_{\text{PD}}^{ - 1} = \tau_{\text{M}}^{ - 1} + \tau_{\text{S}}^{ - 1} = \frac{{V\varpi^{4} }}{{4\uppi v^{3} }}(\varGamma_{\text{M}} + \varGamma_{\text{S}} )$$
where τM and τS are relaxation time of the point defect scattering processes due to mass difference and strain fluctuations, respectively, V is the volume per atom, ΓM and ΓS are the disorder scattering parameters due to mass difference and strain field fluctuations, respectively [31, 32]. The disorder scattering parameters can be deduced by [32]:
$$\frac{{\kappa_{\text{L}} }}{{\kappa_{\text{L}}^{\text{p}} }} = \frac{{\tan^{ - 1} u}}{u},u^{2} = \frac{{\uppi \theta_{\text{D}} \mathrel\backepsilon }}{{hv^{2} }}\kappa_{\text{L}}^{\text{p}} (\varGamma_{\text{M}} + \varGamma_{\text{S}} )$$
where \(\kappa_{\text{L}}\), \(\kappa_{\text{L}}^{\text{p}}\), u and \(\mathrel\backepsilon\) are the lattice thermal conductivity of the crystal with disorder, the lattice thermal conductivity of the crystal without disorder, the disorder scaling parameter and the average volume/atom, respectively. The disorder scattering parameters of pristine and S/Sm co-doped Cu3SbSe4 calculated according to the reference value are listed in Table 3.
Table 3

Calculated disorder scattering parameters of pristine and doped Cu3SbSe4 specimens according to values from Ref. [30]


Calculated \(\varGamma_{\text{M}} + \varGamma_{\text{S}}\)





















In addition to Umklapp and point defect scattering, it was also estimated the contribution of boundary scattering to κL. The relaxation time of boundary scattering is given by τBS = d/v [33], where d is the average grain size of the sample. Based on XRD and SEM results (Fig. 1b), a value of d = 10–30 μm is estimated.

Figure 6a shows the room temperature lattice thermal conductivities calculated using the Callaway model on the assumption of combined scattering mechanisms (U, PD and B) according to the data from Ref. [30]. Figure 6b plots the calculated phonon relaxation time versus frequency of point defect scattering at 325 K for S-doped Cu3SbSe2.85S0.15 and S/Sm co-doped Cu2.9925Sm0.0075SbSe2.85S0.15. As shown in Fig. 6a, b, considering the PD contribution, κL of the Cu3−xSm x SbSe4−yS y (x = 0 and y = 0, 0.05, 0.10 and 0.15) samples decreases with S content increasing due to S doping-induced point defect scattering, so the phonon relaxation time of S-doped Cu3SbSe2.85S0.15 is much smaller than that of the pristine sample. Compared with the S-doped sample, in the S/Sm co-doped samples, the lattice thermal conductivity should be lower (the bottom line in Fig. 6a) and the phonon relaxation time should be shorter (the bottom line in Fig. 6b) due to enhanced point defect scattering by Sm doping.
Fig. 6

a Calculated lattice thermal conductivities of specimens at 325 K based on data from Ref. [30] on assumption of different scattering mechanisms (U: Umklapp scattering, PD: point defect scattering, B: boundary scattering); b calculated phonon relaxation time versus frequency of point defect scattering for S-doped Cu3SbSe2.85S0.15 and co-doped CSS:(Sm-x,S-y) at 325 K according to Ref. [30]; c comparison of experimental and calculated lattice thermal conductivities for specimens CSS:(Sm-x,S-y) (x = 0, 0.005, 0.0075 and y = 0.15) at 325 K

The Sm content-dependent κL of Cu3−xSm x SbSe3.85S0.15 (x = 0, 0.0050, and 0.0075) samples are shown in Fig. 6c. The experimental results are close to the bottom pink line calculated according to the data from Ref. [30]. The experimental data does not match very well with the calculated results. The inconsistency might be due to differences between the actual Debye temperature and sound velocity of the as-prepared samples and the data of Ref. [30]. Nevertheless, the trend of the experimental and the calculated κL data of Cu3−xSm x SbSe3.85S0.15 (x = 0, 0.0050, and 0.0075) samples are similar and the κL values equally decrease with doping content increasing due to the point defect scattering contribution.

3.4 Figure of Merit

The ZT values of all samples are displayed in Fig. 7. Although the PF values of doped samples are lower than that of pristine Cu3SbSe4, the ZT values of most of the doped samples are higher than that of pristine Cu3SbSe4 due to the fact that S and/or Sm doping increases point defect scattering. Specifically, ZT = 0.55 is obtained at 648 K for the sample with the nominal composition of Cu2.995Sm0.005SbSe3.95S0.05, amounting to a 55% increase compared to that of pristine Cu3SbSe4 studied here.
Fig. 7

Temperature dependence of figure of merit (ZT) of a CSS:(Sm-x,S-y) (x = 0 and y = 0, 0.05, 0.10, 0.15), b CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.05), c CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.10) and d CSS:(Sm-x,S-y) (x = 0, 0.0050, 0.0075 and y = 0, 0.15)

4 Conclusion

In summary, the thermoelectric properties of Sm and S co-doped copper antimony selenides were studied in the temperature range of 300 K < T < 650 K. The thermoelectric performance increases as a result of a drastic reduction in the thermal conductivity attributed to an enhanced point defect scattering of heat-carrying phonons. Sm doping introduces additional mass and strain field fluctuations, further reducing the low lattice thermal conductivity of the S-doped samples. As a result, a ZT of ~ 0.55 at 648 K is attained for the sample with nominal composition of Cu2.995Sm0.005SbSe3.95S0.05, which corresponds to an almost 55% increase compared to the ZT of the pristine Cu3SbSe4 studied here.



This work was financially supported by the German Research Foundation within the DFG Priority Program SPP 1386 (No. WE 2803/2-2) and Federal Ministry for Economics Affairs and Energy (BMWI) (No. Nr 19U15006F). We also thank Dr. Angelika Veziridis for intensive discussions on the manuscript.


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Copyright information

© The Nonferrous Metals Society of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Materials ScienceUniversity of StuttgartStuttgartGermany
  2. 2.Key Laboratory of Materials Physics, Institute of Solid State PhysicsChinese Academy of SciencesHefeiChina

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